Question

A shot put is a metallic sphere of radius 4.9 cm. If the density of the metal is 7.8 g per cubic cm., find the mass of the shot put. (Take $\pi =\dfrac{22}{7}$)

Answer 1

Hint: First, find the volume of the shot put by using the formula Volume of a sphere = $\dfrac{4}{3}\pi {{r}^{3}}$. Next, use the formula Density = \[\dfrac{\text{Mass}}{\text{Volume}}\]. We are given the density of the metal and we found the volume in the previous step. Substitute them in the formula and find mass which is our final answer.

Complete step-by-step answer:
In this question, we are given that a shot put is a metallic sphere of radius 4.9 cm. The density of the metal is 7.8 g per cubic cm.
We need to find the mass of the shot put.
To find the mass of the shot put, we need to find the volume of the shot put.
Since, the shot put is a sphere, so we will use the formula for volume of a sphere to calculate the volume of the shot put.
Volume of a sphere = $\dfrac{4}{3}\pi {{r}^{3}}$, where r is the radius of the sphere.
In our question, we are given that r is 4.9 cm. Substituting this in the above formula, we will get the following:
Volume of the shot put = $\dfrac{4}{3}\pi {{\left( 4.9 \right)}^{3}}=\dfrac{4}{3}\times \dfrac{22}{7}\times 4.9\times 4.9\times 4.9=493$ cubic cm.
Now, we know that density is the result of division of mass by volume.
i.e. Density = \[\dfrac{\text{Mass}}{\text{Volume}}\]
Using this formula, we will get the following:
\[7.8=\dfrac{\text{Mass}}{493}\]
Mass = $7.8\times 493=3845.44$ grams.
Hence, the mass of the shot put is 3845.44 grams.
This is our final answer.

Note: In this question, it is very important to know the following: Volume of a sphere = $\dfrac{4}{3}\pi {{r}^{3}}$, where r is the radius of the sphere, and that density is the result of division of mass by volume. i.e. Density = \[\dfrac{\text{Mass}}{\text{Volume}}\]. Without these, you will not be able to solve this question.